Solving for x in the Equation 60/100 × x - y 20/10 y

Mathematics plays a crucial role in many fields, from engineering to finance. Understanding algebraic equations and their solutions is fundamental to this knowledge. In this article, we will walk through the steps to solve a specific equation to find the value of x. The equation is:

60/100 × x - y 20/10 y

Step-by-Step Solution

Let's begin by breaking down and solving the equation step by step:

1. Simplify the Equation

60/100 × x - y 20/10 y

First, let's simplify the fractions:

This simplifies to:

6/10 × x - y 2/10 y

We can further simplify this to:

3/5 × x - y 1/5 y

2. Combine Like Terms

Next, we want to combine like terms on one side of the equation:

3/5 × x - y - 1/5 y 0

Since y has a coefficient in both terms, we can combine the y terms by adding their coefficients:

3. Isolate x

Now, we want to isolate x. First, let's gather all terms involving x on one side and all other terms on the other side:

3/5 × x y 1/5 y

To combine the y terms, we add their coefficients:

3/5 × x 6/5 y

To isolate x, we can multiply both sides by the reciprocal of 3/5:

Multiply both sides by 5/3:

x (6/5 y) × (5/3)

Notice that 5 cancels out:

x 2/3 y

4. Verification

Let's verify the solution by substituting x -2y back into the original equation:

60/100 × (-2y) - y 20/10 y

Simplify the left side:

This simplifies to:

-12/10 y - y 2/10 y

Further simplification gives:

-12/10 y - 10/10 y 2/10 y

-22/10 y 2/10 y

This confirms that our solution is correct.

Conclusion

The value of x is dependent on the value of y. For y -1, x 2/3. As the value of y changes, the value of x also changes accordingly. This problem demonstrates the importance of algebraic manipulation in solving equations.

Keywords

algebra, equation solving, mathematical problem solving